The Elements of Dynamic Symmetry

By Jay Hambidge

Is design intuitive or is it consciously and methodically worked out? Are there basic rules governing design that, when learned, will facilitate the creative process? These questions have been asked by artists, art historians, and art critics throughout the ages.
Convinced that design was not purely instinctive, Jay Hambidge (1867–1924) spent much of his life searching for the technical bases of design. He found his answer in dynamic symmetry, one of the most provocative and stimulating theories in art history. Hambidge's study of Greek art convinced him that the secret of the beauty of Greek design was in the conscious use of dynamic symmetry — the law of natural design based upon the symmetry of growth in man and in plants. But Hambidge, who was not only a theoretician but also a practicing artist, did much more than analyze classical art and its principles of design: he worked out a series of root rectangles that the artist, using the simple mathematics supplied in this book, can easily follow and apply in his own work.
Originally published as a series of lessons in Hambidge's magazine, The Diagonal, this engrossing book explains all the basic principles of dynamic symmetry. Part I sets forth the fundamental rectangles with their simple divisions based on the proportioning law found in nature; Part II explains compound rectangles, many of which were taken from or suggested by analysis of objects of Greek art.
Whether read for its historical importance in art theory, for its illuminating insights into Greek art, or for its practical value to today's artists and commercial designers, The Elements of Dynamic Symmetry has much to offer anyone who is interested in the principle of design.

• Language: English
• Publisher: Dover Publications
• Release date: May 4, 2012
• ISBN: 9780486140254

Jay Hambidge

Jay Hambidge (1867–1924) was a Canadian-born American artist who formulated the theory of "dynamic symmetry", a system defining compositional rules, which was adopted by several notable American and Canadian artists in the early 20th century.

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9780486140254

Reprinted from The Diagonal, copyright, 1919, 1920 by Yale University Press. Copyright © 1926, 1953 by Mrs. Jay Hambidge.

All rights reserved under Pan American and International Copyright Conventions.

This Dover edition, first published in 1967, is an unabridged and unaltered republication of the work originally published by Brentano’s, Inc. in 1926 and reprinted in 1948 by the Yale University Press.

Standard Book Number: 486-21776-0

Library of Congress Catalog Card Number: 66-30210

Manufactured in the United States of America

Dover Publications, Inc.

31 East 2nd Street, Mineola, N.Y. 11501

Table of Contents

DOVER BOOKS ON ART INSTRUCTION

Title Page

Copyright Page

PREFACE

Praise

INTRODUCTION - Synthesis and Analysis.—The Difference between Static and Dynamic Symmetry.—Sources for the Study of Dynamic Symmetry.

THE ELEMENTS OF DYNAMIC SYMMETRY - THE DYNAMIC SYMMETRY OF THE PLANT

PART I - SIMPLE RECTANGLES

LESSON 1 - The Square (1 or Unity).

LESSON 2 - The Rectangle of the Whirling Squares (1.618) and the Root-Five Rectangle (2.236).

LESSON 3 - The Application of Areas.

LESSON 4 - The Reciprocal.

LESSON 5 - The Diagonal.

LESSON 6 - The Root-Two Rectangle (1.4142).

LESSON 7

LESSON 8 - The Root-Three Rectangle (1.732).

LESSON 9 - The Root-Four Rectangle (2.).

LESSON 10 - The Root-Five Rectangle (2.236).

LESSON 11 - The Spiral and Other Curves of Dynamic Symmetry.

LESSON 12 - General Constructions for Similarity of Figure.

PART II - COMPOUND RECTANGLES

LESSON I - The Complement.

LESSON II - Rhythmic Themes of the Whirling Square Rectangle.

LESSON III - The Square Plus a Root-Five Rectangle (1.4472) and a Whirling Square Rectangle Applied to a Square.

LESSON IV - Compound Rectangles Within a Square.

LESSON V - Further Analyses of the Square.

LESSON VI - The Addition of Unity to Dynamic Areas.

LESSON VII - The Gnomon.

LESSON VIII - Ratios Most Frequently Used, Their Reciprocals and Simple Divisions.

LESSON IX - Ratios Most Frequently Used, Their Reciprocals and Simple Divisions.

WHAT INSTRUMENTS TO USE AND HOW TO USE THEM

DEFINITIONS

GLOSSARY

A CATALOG OF SELECTED DOVER BOOKS IN ALL FIELDS OF INTEREST

PREFACE

THESE lessons have been taken from The Diagonal, a monthly magazine which Mr. Hambidge published while he was in Europe during the winter of 1919—20 at the request of students of dynamic symmetry, who were anxious to follow his research work in the museums there. Under the title of the Elements a lesson was given each month that the analyses of various objects might be understandable to the readers who were unfamiliar with the idea.

Except for a rearrangement in the sequence of the lessons no change has been made in the text. Fig. 2a-e of Lesson 1, Figs. 13 and 19 of Lesson 5, Fig. 28c of Lesson 6, Fig. 31b of Lesson 7 and Fig. 46b of Lesson 9 are the only new diagrams which have been added.

The book has fallen naturally into two parts: Part I contains the fundamental rectangles with their simple divisions based on the proportioning law found in nature; Part II the compound rectangles with their more subtle subdivisions, many of which were taken from or suggested by analysis of objects of Greek art. The elementary principles in Part I will give the student a working use of the idea. Much of Part II may be used for reference and for further study.

The simple mathematics necessary to an understanding of the elements of dynamic symmetry can be found in the book. The Definitions, selected from the Thirteen Books of Euclid’s Elements and added at the end of the lessons, will explain most of the geometrical expressions used.

Dynamic symmetry is not a ‘short cut’ to artistic expression and mechanical devices such as ‘triangles’ and ’golden compasses,’ logical substitutes for thinking, in a machine enslaved age, defeat its object. The actual process of studying and understanding the working of a natural design law, opens up a world of new ideas and frees the mind for real creation. Its very impersonal element encourages originality and precludes imitation. Knowledge of a basic law gives a feeling of sureness which enables the artist to put into realization dreams which otherwise would have been dissipated in uncertainty.

INTRODUCTION

Synthesis and Analysis.—The Difference between Static and Dynamic Symmetry.—Sources for the Study of Dynamic Symmetry.

THE basic principles underlying the greatest art so far produced in the world may be found in the proportions of the human figure and in the growing plant. These principles have been reduced to working use and are being employed by a large number of leading artists, designers, and teachers of design and manual art.

The principles of design to be found in the architecture of man and of plants have been given the name Dynamic Symmetry. This symmetry is identical with that used by Greek masters in almost all the art produced during the great classical period.

The synthetic use of these design principles is simple. The Greeks probably used a string held in the two hands. The Harpedonaptae or rope-stretchers of Egypt had no other instrument for orientating and surveying or laying out temple plans. The recovery of these design principles by analysis is difficult, requiring special talent and training, considerable mathematical ability, much patience and sound aesthetic judgment. The analysis of the plan of a large building, such for example as the Parthenon, often is not so difficult as the recovery of the plans of many minor design forms. Sometimes a simple vase is most baffling, requiring days of intensive inspection before the design theme becomes manifest.

To recover these themes of classic design it is necessary to use arithmetical analysis. Geometrical analysis is misleading and inexact. Necessity compelled the old artists to use simple and understandable shapes to correlate the elements of their design fabrics. It is evident that even the simplest pattern arrangements can become very complicated as a design develops. A few lines, simple as a synthetic evolution, may tax the utmost ingenuity to analyze.

The determination of the form principles in a specific example of design means, in a sense, the elimination of the personal element.

With this element removed the residue represents merely the planning knowledge possessed by the artist. This residue is sometimes meagre and more or less meaningless; often it is rich in suggestion and positive design knowledge. Invariably the higher or more perfect the art, the richer is the remainder when the personal element is removed. Also the degree of planning knowledge is positive evidence of the conscious or unconscious use of a scheme in a work of art.

Saracenic, Mahomedan, Chinese, Japanese, Persian, Hindu, Assyrian, Coptic, Byzantine, and Gothic art analyses show unmistakably the conscious use of plan schemes and all belong to the same type. Greek and Egyptian art analyses show an unmistakable conscious use of plan schemes of another type. There is no question as to the relative merit of the two types. The latter is immeasurably superior to the former. This is made manifest as soon as the two types are tested by nature.

These plan schemes, which we find so abundantly in art, are nothing more than symmetry, using the word in the Greek sense of analogy; literally it signifies the relationship which the composing elements of form in design, or in an organism in nature, bear to the whole. In design it is the thing which governs the just balance of variety in unity.

The investigation of this impersonal aspect of art in relation to the symmetry of natural form was begun some twenty years ago. The results of the labor showed clearly that there were but two types of symmetry in nature which could be utilized in design. One of these types, because of its character, was termed static, the other dynamic. Possibly the former is but a special case of the latter, as a circle for example, is a special case of an ellipse. At any rate there is no question of the superiority of the dynamic over the static.

The static is the type which can be used both consciously and unconsciously in art. In fact no design is possible without symmetry. The savage decorating his canoe or paddle, his pottery or his blanket, uses static symmetry unconsciously. The crude drawings of the caveman disclose no design, consequently no symmetry.

As civilization advances the artist becomes more or less conscious of the necessity for symmetry or that quality in a work of art or craft which we recognize as design.

When we reach a period which is recognizable as an art epoch, where a people’s character is shot through and through a great design fabric and the result stands as a national aesthetic expression, we find invariably, a highly sophisticated use of symmetry. But still it is almost always static.

Static symmetry, as the name implies, is a symmetry which has a sort of fixed entity or state. It is the orderly arrangement of units of form about a center or plane as in the crystal. A snow crystal furnishes a perfect example. It is apparent in cross sections of certain fruits. Diatoms and radiolaria supply other examples. It is the spontaneous type; i.e., an artist or craftsman may use it unconsciously.

Static symmetry, as used by the Copts, Byzantines, Saracens, Mahomedans and the Gothic and Renaissance designers, was based upon the pattern properties of the regular two-dimensional figures such as the square and the equilateral triangle. The static symmetry used by the Greeks, before they obtained knowledge of dynamic symmetry, depended upon an area being divided into even multiple parts, such as a square and a half, three-quarters, one-quarter, one-third, two-thirds, etc.

The Tenea Apollo, a 6th century B. C.